SOLUTION: Solve for x (1) x-1/4-2x-3/3=-1/12 (2) 2/6x-19=3/2x-11 (3) 2x+3/3x+4=7/10

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Solve for x (1) x-1/4-2x-3/3=-1/12 (2) 2/6x-19=3/2x-11 (3) 2x+3/3x+4=7/10       Log On


   

Question 763092: Solve for x

(1) x-1/4-2x-3/3=-1/12
(2) 2/6x-19=3/2x-11
(3) 2x+3/3x+4=7/10
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x

(1) x-1/4-2x-3/3=-1/12
x - 1/4 - 2x - 1 = -1/12\
-x - 5/4 = -1/12
-x = -1/12 + 5/4 = -1/12 + 15/12
-x = 14/12
x = -7/6
======================
(2) 2/6x-19=3/2x-11
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Multiply thru by 6x
2 - 19*6x = 9 - 11*6x
2 - 114x = 9 - 66x
2 = 9 + 48x
48x = -7
x = -7/48
=============================
(3) 2x+3/3x+4=7/10
2x + 1/x + 4 = 7/10
2x + 1/x = -33/10
2x%5E2+%2B+%2B+33x%2F10+-+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3.3x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283.3%29%5E2-4%2A2%2A-1=18.89.

Discriminant d=18.89 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3.3%2B-sqrt%28+18.89+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283.3%29%2Bsqrt%28+18.89+%29%29%2F2%5C2+=+0.261565690605037
x%5B2%5D+=+%28-%283.3%29-sqrt%28+18.89+%29%29%2F2%5C2+=+-1.91156569060504

Quadratic expression 2x%5E2%2B3.3x%2B-1 can be factored:
2x%5E2%2B3.3x%2B-1+=+%28x-0.261565690605037%29%2A%28x--1.91156569060504%29
Again, the answer is: 0.261565690605037, -1.91156569060504. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3.3%2Ax%2B-1+%29

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